Probability question

[RB574]

Hi,

If we have A, B, C, D, E and we want to know the probability of picking A and B out of A, B, C, D and E, then will the answer be:

Probability of picking A and Probability of picking B (knowing that A has already been picked) + Probability of picking B and Probability of picking A (knowing that B has already been picked) = 1/5 * 1/4 + 1/5 * 1/4 = 1/10 (since the order matters)
OR
Probability of picking A and Probability of picking B (knowing that A has already been picked) = 1/5 * 1/4 = 1/20 (since the order does not matter)
?

Thanks!

[tim]

The two examples you provided should have looked like this:

ORDER MATTERS
probability of picking A first and then picking B from what's left + probability of picking B first then picking A from what's left =
1/5*1/4 + 1/5*1/4 = 1/20 + 1/20 = 1/10

ORDER DOESN'T MATTER
probability of picking either A or B first and then picking the remaining one from what's left =
2/5*1/4 = 2/20 = 1/10

Notice that we get 1/10 either way. If you are going to adopt the perspective that order doesn't matter (either perspective is fine of course, so it's your choice), your first fraction has to be 2/5, not 1/5. This is because if order doesn't matter you could pick either A or B first.